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摘要翻译：
我们研究了收益的横截面分布的性质。色散与横截面峰度之间存在显著的反相关关系，恐慌时色散高而峰度低，正常时则相反。在恐慌时期，股票收益的共同变动也会增加。我们定义了一个简单的统计量$S$，即给定一天的收益率符号的归一化和，来捕捉系统中的相关性程度。$S$可以看作是系统的序参量，因为如果$S=0$，则没有相关性（无序状态），而对于$S\ne0$，则股票之间有相关性（有序状态）。我们类比非平衡相变，假设当外部波动感知超过某个临界值时，金融市场发生自组织。事实上，美元新元的分布在正常时期是单峰分布，在恐慌时期转向双峰分布。这与二级相变相一致。股票联合随机过程的模拟在时间方向上使用多时间尺度过程，并使用横截面相关性动力学的序参量$S$方程。数值结果表明，无论是在正常情况下还是在恐慌情况下，都与真实数据的程式化事实有很好的定性一致性。
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英文标题：
《Statistical Signatures in Times of Panic: Markets as a Self-Organizing
System》
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作者：
Lisa Borland
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最新提交年份：
2009
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Quantitative Finance 数量金融学
二级分类：General Finance 一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
We study properties of the cross-sectional distribution of returns. A significant anti-correlation between dispersion and cross-sectional kurtosis is found such that dispersion is high but kurtosis is low in panic times, and the opposite in normal times. The co-movement of stock returns also increases in panic times. We define a simple statistic $s$, the normalized sum of signs of returns on a given day, to capture the degree of correlation in the system. $s$ can be seen as the order parameter of the system because if $s= 0$ there is no correlation (a disordered state), whereas for $s \ne 0$ there is correlation among stocks (an ordered state). We make an analogy to non-equilibrium phase transitions and hypothesize that financial markets undergo self-organization when the external volatility perception rises above some critical value. Indeed, the distribution of $s$ is unimodal in normal times, shifting to bimodal in times of panic. This is consistent with a second order phase transition. Simulations of a joint stochastic process for stocks use a multi timescale process in the temporal direction and an equation for the order parameter $s$ for the dynamics of the cross-sectional correlation. Numerical results show good qualitative agreement with the stylized facts of real data, in both normal and panic times.
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PDF链接：
https://arxiv.org/pdf/0908.0111
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